A local gift shop sold bags of candy and cookies for Halloween. Bags of candy cost $$7.50$, and bags of cookies cost $$2.50$, and sales equaled $$27.50$ in total. There were $3$ more bags of cookies than candy sold. Find the number of bags of candy and cookies sold by the gift shop.
Let $x$ equal the number of bags of candy and $y$ equal the number of bags of cookies. The system of equations is then: ${7.5x+2.5y = 27.5}$ ${y = x+3}$ Since we already have solved for $y$ in terms of $x$ , we can use substitution to solve for $x$ and $y$ Substitute ${x+3}$ for $y$ in the first equation. ${7.5x + 2.5}{(x+3)}{= 27.5}$ Simplify and solve for $x$ $ 7.5x+2.5x + 7.5 = 27.5 $ $ 10x+7.5 = 27.5 $ $ 10x = 20 $ $ x = \dfrac{20}{10} $ ${x = 2}$ Now that you know ${x = 2}$ , plug it back into $ {y = x+3}$ to find $y$ ${y = }{(2)}{ + 3}$ ${y = 5}$ You can also plug ${x = 2}$ into $ {7.5x+2.5y = 27.5}$ and get the same answer for $y$ ${7.5}{(2)}{ + 2.5y = 27.5}$ ${y = 5}$ $2$ bags of candy and $5$ bags of cookies were sold.